Orbital confinement fusion device

ABSTRACT

Systems, devices, and methods for generating an orbital confinement fusion reaction are described. An orbital confinement fusion device can include a cathodic inner electrode defining a longitudinal axis of the device. The inner electrode can include an emitter material. The orbital confinement fusion device can include an anodic outer electrode, concentric with the longitudinal axis and defining a chamber between the inner electrode and the outer electrode. The orbital confinement fusion device can also include a plurality of magnetic field generators disposed in a coaxial arrangement relative to the longitudinal axis. The plurality of magnetic field generators can be configured to form a magnetic field parallel to the longitudinal axis in the chamber.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of provisional patent applicationNo. 63/073812, entitled “Controlled Chain-Reaction Fusion Device,” andfiled Sep. 2, 2020, the contents of which are hereby incorporated byreference in their entirety.

BACKGROUND

Nuclear fusion is a reaction in which two or more light atoms combine toform one or more heavier atoms. Due to the mass defect, energy isreleased when elements lighter than iron-56 or nickel-62 are fused asdescribed by E=mc². Nuclear fusion begins when two or more nucleiovercome the coulomb barrier created by repulsive electrostatic forcebetween positive nuclei, bringing the nuclei into spatial proximity.Fusion occurs as a result of quantum tunneling, allowing the nuclei tobind into a nuclide fusion product, and is accompanied by a release offusion energy.

One approach to generating a fusion reaction, referred to asthermonuclear fusion, involves heating fuel atoms beyond ionizationtemperatures, increasing ion density and thermal kinetic energy of theions to the point that fuel nuclei will fuse. In contrast, orbitalconfinement fusion involves accelerating ions to elicit nuclear fusionby increasing the kinetic energies of ions to a point where collisionsresult in nuclear fusion.

Fusion has long been an attractive source of energy as the reaction doesnot produce greenhouse gasses, there is no long-lived radioactive waste,there is a low risk of proliferation, there is no risk of meltdown andthe elements required are widely available and practicallyinexhaustible. Despite being a subject of significant research effortand investment since the theoretical formulation of the physicsunderlying nuclear fusion, methods to initiate, control and maintainfusion reactions to produce useful energy remain elusive. To addresslimitations imposed by electron collisional losses, fusion research hasfocused on thermonuclear fusion. Consequently, fusion reactordevelopment has been dominated by plasma confinement technologies tocontain “hot” plasmas, describing a plasma where electrons and ions arein thermal equilibrium at average temperatures on the order of 100million Kelvin. Controlled thermonuclear fusion involves maintaining hotplasmas at densities and for confinement times for long enough togenerate a positive net energy output, posing a fundamental challenge tothe successful implementation of nuclear fusion.

At the present time, magnetic confinement and inertial confinement arethe main targets of research efforts to achieve controlled thermonuclearfusion. Research into both inertial confinement and magnetic confinementmethods typically involves international and multi-institutionalcollaborative research efforts, resulting in large facilities, capitalinvestments exceeding billions of US dollars, and decades-long designcycles. On a technical level, such projects still struggle with plasmainstability, material limitations, and low energy yields. No fusionreactor has yet to achieve the break-even condition. For at least thesereasons, there is a need for plasma fusion devices that achieve netenergy gain, with a smaller footprint, which can be built and maintainedby individuals or single entities, rather than organizations at theconsortium or government scale.

SUMMARY

This summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This summary is not intended to identify key features ofthe claimed subject matter, nor is it intended to be used as an aid indetermining the scope of the claimed subject matter.

Systems, devices, and methods for generating an orbital confinementfusion reaction are described. An orbital confinement fusion device mayinclude a cathodic inner electrode defining a longitudinal axis of thedevice. The inner electrode may include an emitter material. The orbitalconfinement fusion device may include an anodic outer electrode,concentric with the longitudinal axis and defining a chamber between theinner electrode and the outer electrode. The orbital confinement fusiondevice may also include a plurality of magnetic field generatorsdisposed in a coaxial arrangement relative to the longitudinal axis. Theplurality of magnetic field generators may be configured to form amagnetic field parallel to the longitudinal axis in the chamber.

In some embodiments, the inner and outer electrodes are solids ofrevolution, symmetric about the longitudinal axis, and may be shaped toform a substantially logarithmic electrostatic field in the chamber whenenergized. The inner electrode may be characterized by an aspect ratiogreater than one along the longitudinal axis. The outer electrode mayhave length along the longitudinal axis greater than a largest diameterof the inner electrode. The outer electrode may include a first anodeshell and a second anode shell, disposed laterally relative to thelongitudinal axis and a dielectric insulator disposed between andelectrically isolating the first anode shell and the second anode shell.

In some embodiments, the magnetic field is characterized by a magneticfield strength exceeding a Hull cut-off condition to trap electrons inan orbital path about the inner electrode within the chamber. Theplurality of magnetic field generators may be or include permanentmagnets. The plurality of magnetic field generators may be or includeelectromagnets. The orbital confinement fusion device may also include ahigh voltage power source, electrically coupled with the innerelectrode, and operative in a range from about 50 kV DC to about 4.0 MVDC. The inner electrode may define a first end and a second end. Theorbital confinement fusion device may further include a first dielectricinsulator mechanically coupled with the first end and isolating thefirst end from the outer electrode and a second dielectric insulatordisposed in the chamber between the second end and the outer electrodeand isolating the second end from the outer electrode. The firstdielectric insulator may define an insulating cavity and mayelectrically isolate the high voltage power source from the outerelectrode.

In some embodiments, the outer electrode defines an aperture, analignment of the aperture defining an injection trajectory, theinjection trajectory corresponding to a pitch angle of entry of a stableelliptical orbit of an ion of a given mass-to-charge ratio about theinner electrode. The ion may be, but is not limited to, a proton(m/z=1), a deuterium ion (m/z=2), a tritium ion (m/z=3), lithium-6 ion(m/z=6), or a boron-11 ion (m/z=11). The outer electrode may furtherdefine a port fluidly coupled with the chamber and an externalenvironment. The port may be configured to fluidly couple with a vacuumsystem. The emitter material may be disposed on the inner electrode orintegrated in the inner electrode. The emitter material may beconfigured to inject electrons into the chamber when the inner electrodeis energized. The emitter material may be or include a thermionicemitter material.

In some embodiments, the orbital confinement fusion device furtherincludes an image current device electrically coupled with the outerelectrode and configured to generate electrical energy from a pluralityof charged particles orbiting the inner electrode, the plurality ofcharged particles exhibiting harmonic axial motion aligned with thelongitudinal axis. The orbital confinement fusion device may furtherinclude a fluid conduit disposed in the outer electrode or the innerelectrode. The orbital confinement fusion device may be characterized byphysical dimensions on the order of tens of centimeters. In someembodiments, the orbital confinement fusion device is electricallycoupled with an electrical power system configured to receive electricalpower or heated coolant from the device.

A method of generating orbital confinement fusion energy in a fusiondevice described above may include energizing the inner electrode to avoltage from about 50 kV DC to about 4.0 MV DC, thereby forming alogarithmic electrostatic field between the inner electrode and theouter electrode and injecting a plurality of electrons into the chamber.The method may include injecting a beam of fuel ions into the chamberand at an angle tangential to a surface of the inner electrode, causingthe fuel ions to interact with the electrostatic field and to enter anelliptical orbit about the inner electrode. The method may also includegenerating a magnetic field aligned with the longitudinal axis using theplurality of magnetic field generators, the magnetic field characterizedby an intensity corresponding to a Hull cut-off condition andredirecting the electrons back toward the inner electrode.

In some embodiments, the method further includes flowing a coolantthrough the fluid conduit, heating the coolant through contact with theouter electrode, and generating electricity using the heated coolant.The method may further include applying a radio-frequency (RF) voltagesignal to the outer electrode using a charge image circuit, wherein afrequency of the RF voltage signal corresponds to an oscillation ofcharged particles in the chamber along a direction aligned with thelongitudinal axis. The method may further include generating an RFcurrent using the charge image circuit and generating a direct currentfrom the RF current using an RF-to-DC rectifier circuit.

DESCRIPTION OF THE DRAWINGS

The foregoing aspects and many of the attendant advantages of thisinvention will become more readily appreciated as the same become betterunderstood by reference to the following detailed description, whentaken in conjunction with the accompanying drawings, wherein:

FIG. 1 is a schematic diagram illustrating an example system forgenerating energy using an orbital confinement reactor device, inaccordance with some embodiments of the present disclosure.

FIG. 2A is a schematic diagram illustrating an example reactor deviceincorporating a two-part outer electrode, in accordance with someembodiments.

FIG. 2B is a schematic diagram illustrating the example reactor deviceincorporating a one-part outer anode, in accordance with someembodiments.

FIG. 2C is a schematic diagram illustrating example reactor deviceincorporating a two-part outer anode in three-quarter section, inaccordance with some embodiments.

FIG. 3 is a schematic diagram illustrating an example ion injectionsystem, in accordance with some embodiments.

FIG. 4 is a schematic diagram illustrating the example reactor deviceand magnetic field generator configuration, in accordance with someembodiments.

FIG. 5 is a schematic diagram illustrating an end-view representation ofemitted electron and orbiting ion interactions, in accordance with someembodiments.

FIG. 6 is a graph illustrating reaction rate (ordinate) and density(abscissa) for an example orbital confinement reaction device, at 125keV average electron temperature for three key design points, inaccordance with some embodiments.

FIG. 7 is a block flow diagram illustrating an example process forgenerating energy or neutrons using an orbital confinement reactordevice, in accordance with some embodiments.

Like reference numerals refer to like parts throughout the various viewsunless otherwise specified. Not all instances of an element arenecessarily labeled to reduce clutter in the drawings where appropriate.The drawings are not necessarily to scale, emphasis instead being placedupon illustrating the principles being described.

DETAILED DESCRIPTION

While illustrative embodiments have been illustrated and described, itwill be appreciated that various changes can be made therein withoutdeparting from the spirit and scope of the invention.

Introduction:

The concept of orbital ion confinement was first proposed in 1923 in theKingdon trap. A Kingdon trap consists of a thin central wire, an outercylindrical electrode and isolated end cap electrodes at both ends. Astatic applied voltage between the wire and the electrode results in aradial logarithmic potential therebetween. Ions are stored with a finiteangular momentum about the central wire and the applied electric fieldin the device allows for stable ion trajectories over relatively longperiods of time. The Knight trap, a variant of the Kingdon trap,modifies the outer electrode to confine the ions in orbit about the trapcylindrical axis with harmonic axial motion. The harmonic axial motionis characteristic of the charge-to-mass ratio (Z/m) of the confined ionsand can be measured via image current radio frequency (RF), where acombination of ions of different mass generate a convoluted RF signalthat is deconvoluted using Fourier transfer techniques. The orbitrap isa refinement of the Knight trap geometry that eliminates cross-couplingterms between ion radial and axial motion resulting in a highlysensitive mass spectrometer.

The Kingdon trap, Knight trap, and the orbitrap represent sensitiveinstruments for detecting and differentiating ions by mass but areinherently unable to extract energy or neutrons from nuclear fusion. Thelimitation is due, at least in part, to operating parameters such aspressure, temperature, electrostatic field strength, magnetic fieldstrength, ion density or space charge, ion energy distribution, or thelike. Additionally, ion-mass sensors isolate ions from an ion source,which is typically an ionizing plasma formed using an analyte as inplasma-mass spectrometry systems (e.g., ICP-MS), where the ions are notsuitable fusion fuels. Instead, the space between the electrodes ismaintained free of electrons, which serves at least in part to improvethe sensitivity of the instrument by lowering ion density and increasingharmonic axial motion for improved signal resolution. As such, anorbital confinement fusion device represents a significant departurefrom the structure and operation of an orbitrap-type mass sensor, ratherthan a modification of operating parameters or an inclusion of one ormore discrete structural elements to add new functionality.

Nuclear fusion devices based on orbital confinement, for example,generate energy by stimulating fusion events between light ions to formheavier ions. Described in terms of a fusion reaction rate constant “k,”orbital confinement fusion includes confining fuel and reaction productions together over relatively long periods of time of approximately onesecond or more and relatively long particle track distances on the orderof 1×10⁸ cm. Confining ions in this way serves to increase the number ofenergy transferring scattering events to a point where fusion reactionsbecome more probable, described in terms of collisional cross-sectionsbelow. Orbital ion confinement can achieve ion confinement times,distances, and energies to elicit nuclear fusion. Kingdon/Orbitrap masssensors can achieve relatively high space charges, on the order of2×10¹⁰ atoms/cm³, compared to other ion trap designs, but cannot achievethe space charges generated in an orbital confinement reactor device, onthe order of 1×10¹² -1×10¹⁵ atoms/cm³.

An orbital confinement fusion reactor, by contrast, increases ion spacecharge by introducing and confining electrons in orbit with ions arounda central electrode. Injecting space charges via electrons serves tooffset the positive ion space charge, increasing achievable ion density,at least in part by screening ion-ion repulsion. Electron confinementcan be facilitated by a different physical mechanism than that used forion confinement, as an approach to providing independent control of ionand electron orbits in the device and thereby improving reactor controland improving reactor efficiency. For example, a magnetic field can begenerated parallel to a longitudinal axis of the orbital confinementreactor, as in a magnetron-type magnetic field generator, that exceedsthe Hull cutoff condition, bending electron trajectories in a directionorthogonal to the magnetic field direction, and thereby inducing curvedmagnetron-type motion of electrons around the central electrode in thesame direction as orbiting ions, thereby reducing two-stream instabilityof the ion beam and/or fusion plasma and reducing losses attributable toelectron-ion collisions.

The operating window of fusion reactor devices can be determined atleast in part in terms of a fusion triple product of plasma density,temperature, and confinement time (nTτ). As a figure of merit, thetriple product describes conditions for fusion reactions to occurcontrollably and reproducibly while generating net positive energy,referred to as the Lawson criterion. Density, temperature, andconfinement time can be controlled through operational parameters of thereactor device. For example increasing the ion flux into a fusionreactor from a fuel ion source can increase the plasma density, whileincreasing electrostatic field strength can increase temperature byaccelerating ions to higher average speeds. The parameters are coupled,such that increasing one parameter can affect another parameter. Forexample, increasing plasma density can increase collisional losses andcan reduce confinement time as ions impact reactor surfaces. The tripleproduct can be used to derive electrostatic field strength, magneticfield strength, ion flux, and electron flux parameters for a reactordevice.

In this way, reactor conditions can be brought to a point where nuclearfusion generates net positive energy. In an illustrative example, fuelions are injected tangentially between an inner electrode and an outerelectrode and into an electrostatic field with sufficient energy toassume stable elliptical orbits around the inner electrode. During anelliptical orbit, positively charged fuel ions accelerate towards thenegative inner electrode, converting potential energy into kineticenergy, until reaching the perigee point of the elliptical orbit. Afterreaching perigee, fuel ions decelerate while moving away from thenegative cathode potential and storing potential energy until reachingthe apogee point of the elliptical orbit. A fuel ion completes millionsof such orbits in the reactor over a period of time on the order of onesecond. Additionally, an ions elliptical orbit can cross those of otherions millions of times, increasing the probability of a relativelyunlikely fusion event to occur. Eventually, a fusion event occursbetween fuel ions in colliding orbital trajectories, releasing fusionreaction products, including but not limited to charged particles(alphas, helium-3, protons, tritium, etc.), radiation, and thermalenergy.

After a fusion event, a portion of the fusion reaction charged particlesimpact the electrodes, converting kinetic energy into heat that isdissipated into the device. Additionally, unreacted fuel ions eventuallyimpact the negatively charged electrode, further heating the device.Cooling channels in the reactor can extract heat which can be used togenerate electricity via thermodynamic cycles (e.g., by Seebeckthermoelectric generator devices or heat-exchanger systems). Theremaining fusion reaction product particles assume stable orbits aroundthe negative cathode potential well. Fusion products, travelling fasterthan fuel ions also orbiting the inner electrode, can transfer kineticenergy to the fuel ions via Rutherford upscattering interactions. Aftermultiple ion-ion scattering collisions, the fusion products collide withreactor internal surfaces, generating additional heat. The upscatteredfuel ions follow circular orbits, which increases the effective iontemperature, the reactivity of the fusion plasma, and the overall fusionreaction rate. In this way, the orbital confinement reactor device cansustain nuclear fusion with net-positive energy output that can be usedto generate electricity in a compact footprint.

Fusion Reaction Physical Principles:

The following discussion of principles of an orbital confinement reactordevice is not intended to limit the scope of the present disclosure. Forexample, while discussion of fusion reactions will focus onDeuterium-Deuterium fusion, it is contemplated that the principles areequally applicable to other fusion reactions including but not limitedto proton-boron 11 fusion and deuterium-tritium fusion.

Furthermore, it is contemplated that fusion reactions may be furtheraugmented by multiple steps, whereby a first fusion reaction serves as asource of fuel ions directly in the device, for example, through neutronactivation of Li-6 in an exothermic step that generates energetic alphaparticles and tritium. In this way, the fusion of two or more species,including but not limited to neutrons, protons, deuterium, tritium,helium-3, lithium-6, or boron-11, generates fusion products at elevatedkinetic energy. Fusion products can collide with fuel ions, transferringkinetic energy through upscattering, thereby promoting fuel ions totemperatures with chain reaction potential. In the context ofdeuterium-deuterium fusion (D-D), reactions are approximately equallylikely to follow either of the following paths:D+D→ ₂ ³ He(0.82MeV)+n(2.45MeV) 50%   (1)D+D→ ₁ ³ T(1.01MeV)+p(3.02MeV) 50%   (2)

Upscattering between alpha particle fusion products and fuel ions isdescribed by the following collisional upscattering reaction:₂ ³ He(0.82MeV)+D _(slow)→D _(fast)  (3)

Equation (3) represents collisional up-scattering of deuterons toenergies at which the deuterons can induce follow-on reactions of thetype in Equation (1).

The chain reaction equation for D-D fusion with a helium-3 ->deuteriumup-scattering path is described as follows, the parameters being definedin table 1:

$\begin{matrix}{I_{D} = {I_{{\,_{2}^{3}H}e}n_{D}\sigma_{{{\,_{2}^{3}H}e}\rightarrow D}x_{{\,_{2}^{3}H}e}}} & (4)\end{matrix}$

The up-scattered deuterium current and energy distribution is determinedby Equation (4). The number of fusion events resulting from theup-scattered deuterium current (I_(D)) is defined as follows:

$\begin{matrix}{I_{D - {Dfusion}} = {n_{D}I_{D}\sigma_{D - {Df}}x_{D}}} & (5)\end{matrix}$ $\begin{matrix}{k_{D - {Dfusion}} = \frac{0.5I_{D - {Dfusion}}}{I_{\,_{2}^{3}{He}}}} & (6)\end{matrix}$

TABLE 1 parameter definitions for equations 4-6 I₂ ³ _(He) Initialhelium-3 current e.g. due to thermonuclear reactions (atoms/s) n_(D)Deuterium density (atoms/cm³) σ₂ ³ _(He→D) Helium-3 -> deuteriumRutherford up-scattering cross section (cm²) x₂ ³ _(He) Helium3 atominteraction length/stopping distance (cm) I_(D) Up-scattered deuteriumcurrent (atoms/s) distribution I_(D-Dfusion) Integrateddeuterium-deuterium fusion reaction rate (reactions/s) σ_(D-Df) D-Dfusion cross-sections (cm²) x_(D) Deuterium interaction length/stoppingdistance (cm) K_(D-Dfusion) D-D collisional fusion chain reaction factor

In some embodiments, an orbital confinement fusion reactor functionswith a ratio of fusion reactions over the helium-3 (or alpha particlesfor alternate fuels) current to the positive electrode above unity (e.g.k_(D−Dfusion)>1). In this way, additional energy output can be achieved,after taking into account collisional and other loss mechanisms such asBremsstrahlung radiation and/or confinement losses.

While this disclosure focuses on Deuterium-Deuterium fusion in theprocess description, as an electrostatic ion confinement device thereactor is also capable of operation with any fusion fuel while imposingmagnetic fields for electron confinement. Generally, higher fuel ionenergy and reaction product energy implicates higher electric fieldstrength for positively charged particle confinement, but it isunderstood that the physical principles of electron injection andRutherford upscattering are equally applicable to stimulate additionalnuclear fusion in a variety of fuel ion types for both energy generationand neutron production.

Deuterium-Deuterium and Deuterium-Tritium can be used as fusion fuelsfor high flux neutron production and releases neutrons with a meanenergy of 2.45 MeV (50% branch probability). Deuterium-Tritium fuelsproduce a highly penetrating neutron with a mean energy of 14.1 MeV.Deuterium-Helium3 fusion produces a 4 MeV alpha particle and anenergetic proton (14 MeV) that has applications as a high energy protonbeam source. Proton-Boron 11 fusion produces three alpha particles withan average energy of 2.9 MeV. Such alpha particles may be confined in anorbital confinement reactor, upscatter additional ions to fusionenergies and serve to increase fusion yield. Any of the aforementionedfusion fuels may be used for energy generation or as a neutron sourcefor imaging or the generation of valuable isotopes.

In some embodiments, the orbital confinement reactor generates a plasmain which particles are characterized by stopping distances greater than1E8 cm, and mean generation times (A) on the order of ˜1 s. Theprinciples of stopping distance and mean generation time are describedin more detail in the following paragraphs.

In the context of the present disclosure, stopping distance describes adistance over which a particle loses energy to interactions with matter,such as through collisions with other particles in a plasma. Thestopping distance of ions in a plasma is briefly summarized as follows:

$\begin{matrix}{S = {{- \frac{dE}{\rho{dx}}} = {\frac{K}{AE}\left\lbrack {{\left( {Z - Z^{*}} \right)L_{be}} + {Z^{*}L_{fe}}} \right\rbrack}}} & (7)\end{matrix}$ $\begin{matrix}{{K = \frac{2\pi N_{a}m_{a}}{m_{e}}},\ {E = \frac{m_{a}v_{a}^{2}}{2}}} & (8)\end{matrix}$ $\begin{matrix}{L_{be} = {\ln\left( \frac{2m_{e}v_{a}^{2}}{\overset{\_}{I}} \right)}} & (9)\end{matrix}$ $\begin{matrix}\begin{matrix}{L_{fe} = {{G(x)}{\ln\left( \frac{2m_{e}v_{ae}^{2}}{hw_{pe}} \right)}{where}}} \\{{x = \frac{v_{a}}{\sqrt{\frac{2kT_{e}}{m_{e}}}}},} \\{{{G(x)} = {{{erf}(x)} - {\frac{2}{\sqrt{\pi}}x{\exp\left( {- x^{2}} \right)}}}},} \\{{hw}_{pe} = {3.71 \times 10^{{- 1}1}\sqrt{n_{e}\left( {cm^{- 3}} \right)}eV}}\end{matrix} & (10)\end{matrix}$

TABLE 2 Parameter definitions for equations 7-10 S Stopping distance inMev-cm2/mg N_(a) Avogadro number E Ion kinetic energy where thesubscript a is the fast atom, e.g. ma is the proton mass (a = 1) is1.66e−27 kg, va is the proton velocity (m/s) Z atomic number of theplasma (proton = 1, alpha particle = 2, etc.) Z* average ionizationdegree of the plasma medium the ion is travelling through A element massnumber for the plasma medium m_(e) subscript e signifies electron, inthis case electron mass (me) Ī Mean excitation energy 9 eV for proton xratio of fast ion velocity (va) to electron thermal velocity hw_(pe)plasmon energy in eV v_(ae) the average relative speed between fast ionand plasma electrons

Stopping distances are strongly influenced by the number of electrons(n_(e)) present in the plasma and the plasma electron temperature(T_(e)), as reflected in the definitions of parameters x, and hw_(pe).The electron temperature is directly proportional to the square of theelectron velocity (V_(e)) of the emitted electrons from the emissivecoating scaled by the Boltzmann constant K_(b):

$\begin{matrix}{T_{e} = \frac{mV^{2}}{K_{b}}} & (11)\end{matrix}$

Above electron temperatures of 10,000 eV the stopping power issignificantly reduced, particularly for ion energies below 500 keV.

As previously described, the orbital confinement device can operate atleast in part by accelerating ions through collisional energy transfer.The probability of a particular collision is described by a collisionalcross section, as would be understood by a person having ordinary skillin the art. The cross section for up-scattering a deuterium ion from ahelium-3 particle is governed by the Rutherford differential scatteringequation:

$\begin{matrix}{\sigma_{{\,_{2}^{3}{He}}\rightarrow D} = {\frac{Z_{D}^{2}{Z_{\,_{2}^{3}{He}}^{2}\left( \frac{a\overset{¯}{h⁢c}}{E_{\,_{2}^{3}{He}}} \right)}^{2}}{16{\sin^{4}\left( {\theta/2} \right)}}0.01({barn})}} & (12)\end{matrix}$

TABLE 3 Definitions of parameters in equation 12 a Stopping distance inMev-cm2/mg hc 197.3 MeV fm σ₂ ³ _(He→D) differential cross-section (inbarns) for scattering a deuteron to an energy level corresponding to agiven scatter angle θ E₂ ³ _(He) helium 3 particle energy in MeV Z₂ ³_(He) helium3 particle charge (+2) Z_(D) up-scattered ion charge (+1 fordeuterium)

Collisional energy is transferred from a helium-3 to a deuterium ion viathe full-angle scattering (FAS) method, summarized by the followingequations:

The impact parameter is defined as:

$\begin{matrix}{b_{\bot} = \frac{\left| {q_{i}q_{j}} \right.❘}{4\pi\varepsilon_{o}m_{ij}v_{ij}^{2}}} & (13)\end{matrix}$

Where q is the charge of the particle, ε_(o) the vacuum permittivity,m_(ij) the reduced mass and ν_(ij)=|ν_(i)−ν_(j)| is the relativevelocity between the two particles. The maximum impact parameter is setto the Debye length as follows:

$\begin{matrix}{b_{\max} = {\lambda_{D} = \sqrt{\frac{\varepsilon_{o}k_{B}/q_{e}^{2}}{\frac{n_{e}}{T_{e}} + {\sum_{j}{z_{j}^{2}{n_{j}/T_{i}}}}}}}} & (14)\end{matrix}$

Where k_(B)is the Boltzmann constant, q_(e) the electron charge, n_(e)and n_(j) the electron and ion species (j) number density, T_(e) andT_(i) the electron and ion species temperature and z_(j) the ion speciescharge.

The total Rutherford cross section is defined as:σ_(R) =πb _(max) ²   (15)

And the number of Rutherford scattering events can be determined byN=σ _(R)ν_(ij) n _(j) dt ln∧  (16)

Where dt is the timestep and ln∧ is the well-known Coulomb logarithmdefined as:ln∧=ln√{square root over ((b _(max) ² +b _(™) ² /b _(™) ²)}  (17)

The probability of a single Rutherford event is defined as:P _(R) =σ_(R)ν_(ij) n _(j) dt   (18)

The collisional operator functions by evaluating a non-dimensional pathlength, s, defined as:s=4 πb _(™) ²ν_(ij) n _(j) dt ln∧  (19)

Based on the differential Rutherford scattering equation and thecollisional operator, a significant majority of up-scattering events aresmall angle (<1 keV) in nature. As a result, upscattering a Deuteriumfuel ion to fusion energies involves multiple collisions over a periodof time.

The reaction rate of a self-sustaining collisional up-scattering fusionchain reaction follows an exponential scaling law e^((k−1)τ/Λ)with chainreaction multiplication factor k≥1, t is the elapsed time and Λ is themean generation time:e ^((k−1)τ/Λ)  (20)

When k<1 the reaction is deemed subcritical and the reaction ratedecreases with time. When k>1 the reaction is deemed supercritical andthe reaction rate increases with time. When k=1 the reaction is deemedcritical and the reaction rate is steady with time. The mean generationtime Λ determines how quickly the reaction progresses but not the steadystate value once k=1. Mean generation time scales with the stoppingdistance of the Helium-3 in the plasma.

For Deuterium ions in thermal equilibrium with free electrons in theplasma (T_(i)=T_(e)), increasing the electron temperature and/or theelectron density increases the energy transfer ratio between electronsand ions, until the Deuterium ion velocities starts to match theHelium-3 velocity, above which the energy transfer ratio decreases.

Operation Of An Orbital Confinement Reactor:

In contrast to thermonuclear fusion, orbital confinement reactorsconfine ions in orbits at defined energies with non-Maxwellian energydistributions. As such, the fusion reaction rate (referred to as“dn/dt”) in units of reactions per second is governed by recirculatingbeam fusion physics, described by the following expression:

$\begin{matrix}{\frac{dn}{dt} = {\sigma\frac{N^{2}}{S}f_{recirculation}}} & (21)\end{matrix}$

Where σ is the Deuterium beam cross-section at a given energy level, Sis the interaction area, ƒ_(recirculation) is the recirculationfrequency and N is the number of fuel ions in the reactor. For acylindrical Kingdon/Orbitrap type configuration the key parameters arer_(i), the inner cathode stalk radius and r_(o) the outer anode innersurface radius and finally 1, the length of the reactor. The interactionarea (S) and recirculation frequency (ƒ_(recirculation)) are defined as:

$\begin{matrix}{{S = {\left( {r_{o} - r_{i}} \right)l}}} & (22)\end{matrix}$ $\begin{matrix}{f_{recirculation} = \frac{v_{i}}{2{\pi\left( {{{0.5}r_{o}} + {{0.5}r_{i}}} \right)}}} & (23)\end{matrix}$

Where v_(i) is the Deuterium ion velocity at a given energy. The totalspace charge in the reactor is a fixed limit. Consequently, as thenumber of confined fusion reaction charged particles such as Helium-3increase, the number of total fuel ions decreases to compensate andmaintain the space charge limit. In some embodiments, fuel ionconcentration is controlled through a fuel ion flux into the reactor.The number of Deuterium ions that can participate in fusion reactions isdefined as:

$\begin{matrix}{N = {N_{ion} - N_{{Helium}3}}} & (24)\end{matrix}$ $\begin{matrix}{N_{ion} = {Vn_{i}}} & (25)\end{matrix}$ $\begin{matrix}{N_{{Helium}3} = {0.5Z_{{Helium}3}\frac{dn}{dt}\Lambda}} & (26)\end{matrix}$

Where N_(ion) is the space charge limited number of ions in the reactorobtained from the reactor volume (V) and the limit ion number densityn_(i). The number of helium ions present in the reactor is defined asN_(Helium3) where dn/dt is the reaction rate, the 0.5 represents the DDfusion 50% reaction probably for Helium-3, Z_(Helium3) the+2 charge andthe mean generation time of ˜1 s.

The Helium-3 reaction products can transfer kinetic energy to Deuteriumfuel ions, thereby increasing the fusion cross-section, representingreaction probability. This is offset by the fact that as the number ofHelium-3 ions in the reactor goes up, the total number of Deuterium ionsmust decrease to maintain space charge limits. Within the context of achain reaction, the k-factor in Equation (20) can be evaluated based onthe gradients of both the fusion reactivity and the total number of fuelions as follows:

$\begin{matrix}{k = \frac{\sigma_{2}N_{2}^{2}}{\sigma_{1}N_{1}^{2}}} & (27)\end{matrix}$

where the numerator σ²N₂ ² describes the fusion cross-section and totalfuel ions after a given time interval with Helium-3 upscattering.Initially, during reactor start-up, the number of fusion reactions andHelium-3 ions are low as are reductions in N. Conversely the gradient infusion cross section is high as the Deuterium ions gain energy andreactivity increases. Depending on the initial ion density, the k-factorcan start-off as a large value and as the fuel ions gain energy thereaction rate increases. Eventually, as the number of Helium-3 increaseduring operation, steady state conditions (k=1) will be reached whenincreases in fusion cross-section are offset by the reduction inavailable fuel ions. The steady state condition in the reactor is acomplex function of the fusion fuel reactivity as ion energy increasesdue to up-scattering, ion fuel flux into the device and multiple lossmechanism that transfer energy out of the plasma and cause the ions tolose energy (down scattering, wall impacts, center electrode impacts,radiation, etc.). At k-factors approximately equal to one (“critical”operation) the reaction rate and power output substantially stable withtime. Stable operation can be maintained by adjusting reactor operationsuch that if the reactor output drops below the target power, operatingparameters are reset to provide a k-factor above one (“supercritical”operation), whereas if the reactor exceeds the target power, operatingparameters are reset to provide a k-factor below one (“sub-critical”operation).

With regard to electron injection, it is understood that the magneticfield can bend the emitted electrodes back toward the cathode, therebyavoiding an arc between the electrodes, if the magnetic field strengthexceeds the Hull cut-off condition. For a given voltage, the magneticfield strength that satisfies the Hull cut-off condition is defined bythe following expression:

$\begin{matrix}{B_{c} = {\frac{mc}{ed^{*}}\sqrt{\frac{2eV}{mc^{2}} + \left( \frac{eV}{mc^{2}} \right)^{2}}}} & (28)\end{matrix}$

where B_(c) is the critical magnetic field, m the mass of the electron,e the electron charge (absolute value), V the voltage applied across thegap, c the speed of light and d* the geometric factor defined as:

$\begin{matrix}{d^{*} = \frac{r_{o}^{2} - r_{i}^{2}}{2r_{o}}} & (29)\end{matrix}$

With regard to direct energy extraction from harmonic axial motion ofions, scattering events between confined fusion reaction products andfuel ions impart axial kinetic energy and harmonic axial motion of theions in the reactor. The frequency of the axial motion is characteristicof the charge-to-mass (Z/m) ratio of an ion. Radio-Frequency (RF) energycan be applied at specific frequencies to the outer electrodes toselectively extract axial motion energy via charge image current, in thereverse process by which mass sensors detect mass-specific RF signalsgenerated by the harmonic axial motion of ions.

Application of out-of-phase RF signals to the outer electrodes permitsthe harmonic axial motion of the ions to be de-excited. As collisionsbetween fusion products and fuel ions occur some of the collision energyis transferred to axial motion. RF applied to the outer electrodes canbe used to selectively extract energy from the fuel ions, reactionproducts or both as they oscillate axially between the two halves of theouter electrode. The AC charge image signal can also be rectified to DCcurrent, to charge energy storage devices such as batteries or to poweran electrical load.

The frequency of the axial oscillation is characteristic of the ionmass-to-charge ratio and is determined from the following equation:

$\begin{matrix}{\omega = \sqrt{\frac{kq}{m}}} & (30)\end{matrix}$where ω is the frequency in radians per second, q is the charge of theion and m is the mass of the ion. The image current signal (I), inducedby the axial ion motion, is determined by the following expression:

$\begin{matrix}{{I\left( {t,r} \right)} \approx {{- {{qN}\omega}}\frac{\Delta z}{\lambda(r)}{\sin\left( {\omega t} \right)}}} & (31)\end{matrix}$where N is the number of ions, Δz is the magnitude of the axial motionand λ(r) depends on the geometry of the trap (λ(r)≈outer radius) and isa function of the trap radius.

Discussion of Orbital Confinement Reactor Systems:

Embodiments of a system and method for generating energy and/orradioisotopes using orbital confinement fusion reactions are describedherein. In the following description numerous specific details are setforth to provide a thorough understanding of the embodiments. Oneskilled in the relevant art will recognize, however, that the techniquesdescribed herein can be practiced without one or more of the specificdetails, or with other methods, components, materials, etc. In otherinstances, well-known structures, materials, or operations are not shownor described in detail to avoid obscuring certain aspects.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the present invention. Thus, theappearances of the phrases “in one embodiment” or “in an embodiment” invarious places throughout this specification are not necessarily allreferring to the same embodiment. Furthermore, the particular features,structures, or characteristics may be combined in any suitable manner inone or more embodiments.

FIG. 1 is a schematic diagram illustrating an example system 100 forgenerating energy using an orbital confinement reactor device 105, inaccordance with some embodiments of the present disclosure. Examplesystem 100 includes multiple reactor devices 105 provided with fuel ionsby fuel ion source(s) 110 and power by power source(s) 115, thermallycoupled with thermal generator(s) 120, and electrically coupled withelectric generator(s) 125, each connected to a distribution system 130.It is understood that while example system 100 describes a multi-reactorsystem, applications are contemplated using a single orbital confinementreactor device 105, for example, for portable and/or mobile powergeneration systems. As described in the preceding sections, examplesystem 100 can be applied to generate isotopes, heat, and/or electricityas carbon-free power, to power large civilian eVTOL and electricaircraft, to power military eVTOL, to generate shipborne power andelectric propulsion for vessels sized from small boats to large ships.

Fuel ion source(s) 110 can be or include different types of ion sourcescapable of generating the fuel ion and supplying it to the examplesystem 100 at energies for orbital capture and subsequent fusion.Example system 100 can also be used, as nonlimiting examples, forportable power generation, robotic chassis and/or exoskeleton powergeneration, mobile power generation, auxiliary Power Unit (APU) powergeneration, distributed power generation in remote locations, and/ortelecom communication tower power in remote locations. Example system100 can also be used, as nonlimiting examples, in range extension forelectric vehicles, small eVTOL and electric air vehicles, local orregional power grids, grid-connected storage, remote and forwardoperating base power generation, containerized mobile power generation,and datacenter backup power generation. As such, example system 100 canfill a role ranging from base load generator to peaking generator,depending on the type of system into which it is integrated.

Example system 100 may initiate and/or maintain nuclear fusion and mayaugment fusion via the collisional upscattering mechanisms describedpreviously. Initiating self-sustaining fusion reactions may include aperiod of sub-critical (e.g., k<1) operation where one or more orbitalconfinement reactor devices 105 draw energy from power source(s) 115. Insome embodiments, each orbital confinement reactor device 105 iselectronically coupled with power source(s) 115. In some embodiments, asubset of orbital confinement reactor devices 105 are electronicallycoupled with power source(s) 115, and startup can include a cascaded orstaggered approach. To that end, example system 100 can include powerelectronics and interconnection systems such that a first orbitalconfinement reactor device 105-1 is electrically coupled with powersource(s) 115, from which power is drawn during startup. As firstorbital confinement reactor device 105-1 reaches criticality (k=1) andproduces net positive energy, one or more orbital confinement reactordevices 105 of example system 100 that are electrically coupled to firstorbital confinement reactor device 105-1 can draw power to initiatestartup. In this way, power drawn from external sources can be reduced,facilitating deployment of example system 100 in areas withoutestablished generating capacity. That being said, in applications whereresponse time is important, each orbital confinement reactor device 105can be individually connected to power source(s) 115 and can eachincorporate control systems to startup in parallel or substantially atthe same time.

Fuel ion source(s) 110 can include one or more types of ion sources,depending at least in part of the application of example system 100. Asdescribed in more detail in the preceding sections, example system 100can be applied to isotope generation, power generation, and/or heatgeneration, among other foreseeable uses. In this way, fuel ionsource(s) 110 can be or include, but are not limited to, sources ofprotons, deuterium, tritium, helium-3, lithium-6, or boron-11. As eachorbital confinement reactor device 105 operates using a source of fuelions that are injected into the fusion plasma during operation, examplesystem 100 includes each orbital confinement reactor device 105operatively coupled with fuel ion source(s) 110. Methods of generatingions include, but are not limited to, electromagnetic ionization of anion source, nuclear reactions such as neutron capture, thermionicemission, field-effect emission, or the like, as would be understood bya person having ordinary skill in the art.

As described in more detail in reference to FIGS. 2-4 , each orbitalconfinement reactor device 105 in example system 100 can maintain acritical fusion reaction (e.g., k≈1) and can extract energy from thefusion plasma. The energy can be extracted as thermal energy resultingfrom ion and electron impact into internal surfaces exposed to plasmas.Such thermal energy can be transferred by fluidly coupling orbitalconfinement reactor device(s) 105 with a heat exchange system andapplying one or more techniques for harvesting electrical energy fromheat thus harvested. For example, where reactor operating temperaturescan be maintained on the order of 1000 K, a coolant can be circulatedthrough one or more components of orbital confinement reactor device(s)105, using heat to generate work. In this way, thermal generators 120can be or include systems including, but not limited to, compressors,turbines, turbomachinery, and/or thermoelectric generators, as well asliquid heat transfer systems for conducting heat from orbitalconfinement reactor device(s) 105 to thermal generator(s) 120.Additionally and/or alternatively, thermal generator(s) 120 can alsoinclude heating systems that use at least a portion of the thermalenergy as a heat source.

In some embodiments, example system 100 includes electric generator(s)125 to directly capture electrical energy from orbital confinementreactor device(s) 105. As described in the preceding sections,collisional energy transfer in a recirculating ion plasma induces axialharmonic motion of ions orthogonal to the applied electric field betweenthe electrodes. The frequency of the axial motion can be in the radiofrequency

(RF) range and can be characteristic of the mass-to-charge ratio of theions. As such, orbital confinement reactor device(s) 105 can eachextract electricity by actively damping axial harmonic motion of ions,and the power thus generated can be converted into useful electricity bypower electronics included as part of electric generators 125. In someembodiments, electric generators 125 include one or more componentsystems to output direct current and/or alternating current electricityfrom the RF power drawn from orbital confinement reactor device(s) 105.For example, electric generators 125 can include RF-to-DC rectifiersystems, such that example system 100 can be used to store electricityin grid storage using multi-cell batteries, liquid metal batteries, orthe like.

Additionally and/or alternatively, example system 100 operates togenerate neutrons for one or more purposes through selection of fuel ionsource(s) 110 and/or operating parameters. In this way, example system100 can be operably coupled with systems for using neutrons inapplications including, but not limited to, formation of radioisotopes,production of hydrogen, treatment of nuclear waste, manufacture oftritium by neutron bombardment of lithium, breeding of nuclear fissionfuel, materials analysis including neutron spectroscopy and/or neutronimaging and/or neutron activation analysis, materials processing byneutron irradiation, detection of materials, medical imaging, medicaltherapy including neutron capture therapy and/or neutron beam therapytesting of materials and components, or other uses in scientificresearch, as would be understood by a person having ordinary skill inthe art.

In some embodiments, example system 100 includes one or more groups oforbital confinement reactor devices 105 applied to one of a number ofuses. For example, one or more orbital confinement reactor devices 105can be used to generate heat, one or more orbital confinement reactordevices 105 can be used to generate electricity, and one or more orbitalconfinement reactor devices 105 can be used to generate neutrons. Insome embodiments, a single orbital confinement reactor device 105 can beused to generate heat and electricity, heat and neutrons, orcombinations thereof. Such versatility in application is facilitated byselection of operating parameters, fuel ion source(s) and internalstructures of orbital confinement reactor device(s) 105, described inreference to FIGS. 2A-6 , below.

FIGS. 2A-2C illustrate an example reactor device 200 including internalstructures for generating and sustaining nuclear fusion and forextracting energy, as described in reference to FIG. 1 , FIG. 2A, andFIG. 2B describe example reactor device 200 in section and focus ondifferent internal structures to simplify description and clarify thevisual illustration. It is understood, however, the example reactordevice 200 includes the structures described in FIG. 2A, FIG. 2B, and/orFIG. 2C, except where inclusion is physically impossible.

FIG. 2A is a schematic diagram illustrating example reactor device 200incorporating a two-part outer electrode 210, in accordance with someembodiments. Example reactor device 200 is an example of orbitalconfinement reactor device(s) 105 of FIG. 2 , configured to be able towithdraw electrical energy by damping harmonic axial motion of ions inthe fusion plasma. The example reactor device 200 includes a cathodicinner electrode (205), an anodic outer electrode (210), magnetic fieldgenerator(s) (215), a high voltage power source (220), and a radiationshield (225).

Example reactor device 200 is configured to generate energy using afusion plasma generated between inner electrode 205 and outer electrode210. To that end, inner electrode 205 defines a longitudinal axis 230 ofexample reactor device 200. Outer electrode 210, in turn, is disposedconcentric with longitudinal axis 230 with an inner diameter greaterthan an outer diameter of inner electrode 205, defining an offsetbetween inner electrode 205 and outer electrode 210. In this way, theelectrode arrangement defines a chamber 235 between inner electrode 205and outer electrode 210. During operation, a fusion plasma is generatedin chamber 230 and maintained at or near criticality through combinedapplication of electric and magnetic fields.

In some embodiments, inner electrode 205 is electrically coupled withhigh voltage power source 220 and is configured to create anelectrostatic field between inner electrode 205 and outer electrode 210.Inner electrode 205 can be or include an emitter material 240 such thatinner electrode 205 acts as a source of free electrons. Emitter material240 can be disposed as an emissive coating on a conductive core. In thisway, emitter material 240 is configured to inject electrons into thechamber 235 when inner electrode 205 is energized and/or heated. Emittermaterial 240 can be or include a refractory material characterized bythermionic emission properties at temperatures characteristic of fusionreactions. Emitter material 240 can be characterized by high electronemission properties either via photoemission, thermionic emission, orfield emission. Emitter material 240 can be or include tungsten,thoriated-tungsten, barium-oxides (e.g. Ba-O), Lanthanum hexaboride(LaB₆), Cerium hexaboride (CeB₆), as well as blends, alloys, composites,or combinations thereof. In the context of example reactor 200,photoemission refers to a material that emits electrons into chamber 235in response to irradiation by energetic photons, such as photonsgenerated by a fusion plasma.

Emitter material 240 is configured to emit electrons approximatelynormal to the longitudinal axis 230, due at least in part to orientationof inner electrode 205 relative to outer electrode 210. As such, innerelectrode 205 is oriented to minimize stopping power losses due tocollisions with orbiting ions, as described in more detail in referenceto FIG. 5 . Advantageously, injecting electrons normally from the innerelectrode 205 and curving electron trajectories in the same direction oforbiting ions via the Lorentz force created by magnetic field generators215 can increase interaction lengths between electrons and ions todistances on the order of 1×10⁸ cm and may increase the probability of afusion reaction (e.g., as described by cross sections for a particularinteraction and/or reaction). Advantageously, injecting electrons inthis way reduces space-charge effects and allows the fusion plasma tobecome denser than with electrostatic ion confinement alone.

For example, at elevated temperatures greater than approximately 1000 K,emitter material 240 emits electrons into chamber 235, reducingspace-charge effects and densifying the plasma beyond the densityprovided by electrostatic ion confinement. Inner electrode 205 can beoperably coupled with one or more heating systems to raise thetemperature of emitter material 240. Elevated temperature can beproduced by several methods and systems, including but not limited to,resistive heating, induction heating, and or through electron and ionbombardment during operation. It is understood that emitter material 240can generate a significant electron current at temperatures below 1000K, such as at operating temperatures of example reactor device 200.

As described previously, ion density and hence power available fromexample reactor device 200 is governed by the number of ions orbitinginner electrode 205 (N). The number of ions can be increased by emittingelectrons from inner electrode 205 to offset space charge limits. Theelectrons can be confined in the reactor for periods of time throughapplication of an axial magnetic field meeting or exceeding the Hullcut-off condition and operating like a Magnetron for electronconfinement. While confined, electrons travel at velocities that reduceelectron drag and stopping power on the fuel and reaction product ions,thus reducing ion kinetic energy loss to electrons and increasing fusionreaction rate and power in the reactor.

Magnetic field generator(s) 215 can be disposed in a coaxial arrangementrelative to the longitudinal axis 230. In this way, magnetic fieldgenerator(s) 215 are configured to form a magnetic field substantiallyparallel to the longitudinal axis 230 in the chamber 235. Magnetic fieldgenerator(s) 215 can be or include electromagnets, permanent magnets, ora combination thereof. Magnetic field generator(s) 215 can apply amagnetic field at a strength ranging from 0.01 Tesla to 10 Tesla.Magnetic field generator(s) 215 can thus serve as a magnetron,generating a magnetic field at strength exceeding the Hull cut-offcondition for a given fusion reaction. As previously described, thefield strength, and thus the operating parameters of magnetic fieldgenerator(s) 215, used to exceed the Hull cut-off condition is specificto each type of fusion reaction. In addition, magnetic field strengthmay be used as a control variable to adjust the k-factor of examplereactor device 200 when in operation, as described in more detail inreference to FIG. 4 .

In some embodiments, inner electrode 205 and outer electrode 210 aresolids of revolution and shaped to be symmetric about longitudinal axis230. In this context, a “solid of revolution” describes a shape that issymmetrical about one or more axes of revolution, for example, asdefined by a two-dimensional shape that is symmetrical about an axis ina plane transecting the axis. In some embodiments, electrodes 205 and210 are solids of revolution that incorporate apertures, orifices,conduits, or other features that are not rotationally symmetrical aboutlongitudinal axis 230, as described in more detail below.

In this way, electrodes 205 and 210 are shaped to form a substantiallylogarithmic electrostatic field in the chamber when energized. Alogarithmic electrostatic field, as previously described, refers to anelectric field generated between electrodes 205-210, with innerelectrode 205 serving as the negative cathode and outer electrode 210serving as the positive anode, where the strength of the electric fieldincreases logarithmically between outer electrode 210 and innerelectrode 205, referring to the positive-to-negative convention forelectric fields.

In some embodiments, inner electrode 205 is characterized by an aspectratio greater than one along longitudinal axis 230. In this context, theterm “aspect ratio” describes a ratio of a first characteristicdimension aligned with longitudinal axis 230 and a second characteristicdimension aligned normal to longitudinal axis 230. For example, whereinner electrode 205 is a solid of revolution that is characterized by aradial dimension that depends on axial position (e.g., r=ƒ(z)), theaspect ratio greater than one describes a structure where the length ofinner electrode 205 is greater than the widest point of inner electrode205. As such, inner electrode 205 may define an axial profile, alonglongitudinal axis 230, that includes one or more regions of greaterwidth and one or more regions of narrower width. For example, innerelectrode 205 may define a lateral profile aligned with longitudinalaxis 230 the includes a taper at each end, such that the width of innerelectrode 205 is wider between the ends than at the ends.

In some embodiments, outer electrode 210 has a length 245 alonglongitudinal axis 230 greater than the largest diameter of innerelectrode 205. For example, outer electrode 210 can be a solid ofrevolution about longitudinal axis 230 and can define a negative spaceabout longitudinal axis 230 that, together with inner electrode 205,defines chamber 235. In the example, outer electrode 210 does notcontact inner electrode 205 along length 245, as illustrated in FIGS.2A-3 .

Outer electrode 210 can include one, two, or more shells that can beused to excite or damp harmonic axial motion of ions parallel tolongitudinal axis 230. In some embodiments, outer electrode includes twoanode shells 210-1 and 210-2, disposed laterally relative tolongitudinal axis 230. As described previously, anode shells 210-1 and210-2 can be solids of revolution, symmetrical about longitudinal axis230, In this context, the phrase “disposed laterally” refers to anodeshells 210-1 and 210-2 being disposed in example reactor device 200 atdifferent and/or non-overlapping positions along longitudinal axis 230.In some embodiments, anode shells 210-1 and 210-2 are connected by animage current circuit 250. In some embodiments, a dielectric insulator255 is disposed between and electrically isolates the anode shells 210-1and 210-2.

In some embodiments, inner electrode 205 and outer electrode 210 areelectrically isolated from each other by a first dielectric insulator260 and a second dielectric insulator 265. First dielectric insulator260 can be mechanically coupled with a first end 270 of inner electrode205 and can electrically isolate high voltage power source 220 fromouter electrode 210. Second dielectric insulator 265 can be disposed inchamber 235 between a second end 275 of inner electrode 205 and outerelectrode 210 and can electrically isolate the second end 275 from outerelectrode 210. First dielectric insulator 260 can define an insulatedcavity 280. High voltage power source 220 can be disposed at leastpartially within insulated cavity 280.

High voltage power source 220 can be or include a direct current voltagesource, including but not limited to a Van de Graaff source, a Pelletronsource, or a solid-state power switching generator. In some embodiments,high voltage power source 220 is electrically coupled with innerelectrode 205 and is operative in a range from about 50 kV DC to about4.0 MV DC. As inner electrode 205 functions both as a source ofelectrons to be injected into cavity 235 and as a source ofelectrostatic field serving to trap ions into orbit around innerelectrode 205, voltage applied to inner electrode 205 by high voltagepower source 220 can be dynamic during one or more stages of operationof example reactor device 200. For example, electron flux and forceapplied to orbiting ions can scale proportionally with applied voltage.As such, applied voltage can be a control parameter for example reactordevice 200. Furthermore, applied voltage can vary based at least in parton the type of ions injected into chamber 235. As previously described,force applied to ions in orbit about inner electrode 205 is a functionof charge-to-mass ratio, such that applied voltage may vary with fuelion mass, fuel ion charge, or a combination thereof.

In this way, high voltage power source 220 can be operative from about50 kV DC to about 4.0 MV DC, about 50 kV DC to about 3.9 MV DC, about 50kV DC to about 3.8 MV DC, about 50 kV DC to about 3.7 MV DC, about 50 kVDC to about 3.6 MV DC, about 50 kV DC to about 3.5 MV DC, about 50 kV DCto about 3.4 MV DC, about 50 kV DC to about 3.3 MV DC, about 50 kV DC toabout 3.2 MV DC, about 50 kV DC to about 3.1 MV DC, about 50 kV DC toabout 3.0 MV DC, about 50 kV DC to about 2.9 MV DC, about 50 kV DC toabout 2.8 MV DC, about 50 kV DC to about 2.7 MV DC, about 50 kV DC toabout 2.6 MV DC, about 50 kV DC to about 2.5 MV DC, about 50 kV DC toabout 2.4 MV DC, about 50 kV DC to about 2.3 MV DC, about 50 kV DC toabout 2.1 MV DC, about 50 kV DC to about 2.1 MV DC, about 50 kV DC toabout 2.0 MV DC, about 50 kV DC to about 1.9 MV DC, about 50 kV DC toabout 1.8 MV DC, about 50 kV DC to about 1.7 MV DC, about 50 kV DC toabout 1.6 MV DC, about 50 kV DC to about 1.5 MV DC, about 50 kV DC toabout 1.4 MV DC, about 50 kV DC to about 1.3 MV DC, about 50 kV DC toabout 1.2 MV DC, about 50 kV DC to about 1.1 MV DC, about 50 kV DC toabout 1.0 MV DC, about 50 kV DC to about 0.9 MV DC, about 50 kV DC toabout 0.8 MV DC, about 50 kV DC to about 0.7 MV DC, about 50 kV DC toabout 0.6 MV DC, about 50 kV DC to about 0.5 MV DC, about 50 kV DC toabout 0.4 MV DC, about 50 kV DC to about 0.3 MV DC, or about 50 kV DC toabout 0.2 MV DC, including fractions or interpolations thereof. Forexample, in some embodiments, high voltage power source 220 applies anegative voltage of about 650 kV DC to inner electrode 205. In thiscontext, the term “about” is used to indicate a value within 10% of thestated value. For example, a stated value of about 650 kV is used toindicate a value from 585 kV DC to 715 kV DC. It is understood that thevalues are given as magnitudes without reference to polarity. Forexample, inner electrode 205 can be biased negatively relative to outerelectrode 210, such that the applied voltage supplied by high voltagepower source 220 to inner electrode 205 is negative.

Radiation shield 225 can be or include structural elements of examplereactor device 200, or additional material, including but not limited tolead or tungsten shielding, water pools, or the like. Example reactor200 may be at least partially surrounded by radiation shield 225, suchthat radiation shield 225 can be used to absorb and lower potentiallyharmful radiation. While nuclear fusion produces few to no long-livedradioactive biproducts, energetic particles may be produced and maytransit the physical enclosure of example reactor device 200. As such,radiation shield 225 may be or include materials selected to absorbforeseeable energetic particles, based at least in part on the mode ofoperation of example reactor device 200. For example, where examplereactor device 200 is configured to generate radioisotopes for medicaluse, radiation shield 225 can be structured to absorb energeticneutrons.

FIG. 2B is a schematic diagram illustrating example reactor device 200incorporating a one-part outer anode 205, in accordance with someembodiments. As illustrated in FIG. 2A, example reactor device includesinner electrode 205, outer electrode 210, magnetic field generators 215,high voltage power source 220, and radiation shield 225. In FIG. 2B,example reactor device 200 is illustrated including fluid conduit(s)285, aperture(s) 290, and port(s) 295. While discussion of examplereactor device 200 focused on a configuration including a two-part outerelectrode 210, example reactor device 200 can also include a one-partouter electrode 210, as illustrated in FIG. 2B. It is contemplated thatfluid conduit(s) 285, aperture(s) 290, and/or port(s) 295 can beincluded in either configuration, as well as other electrodeconfigurations with more parts.

Fluid conduit(s) 285 can be integrated into inner electrode 205, outerelectrode 210, radiation shield 225, or a combination thereof. As shown,fluid conduit(s) 285 define one or more channels within outer electrode210. In this way, fluid conduit(s) 285 can define one or more coolantloops through outer electrode 210, through which a coolant can flow. Thecoolant, in turn, can carry heat out of example reactor device 200, andcan transfer the heat into a working fluid, via a heat exchangerexternal to example reactor device 200, to drive thermal generator(s)120 of FIG. 1 . Similarly, fluid conduit(s) can be coupled, directly orvia a heat exchanger, with thermoelectric generators, turbines, and/orturbomachinery, such that heat generated internal to example reactordevice 200 can be removed. Advantageously, fluid conduit(s) 285 can bothextract usable energy from example reactor device 200 and can also serveto control operating parameters. In an illustrative example, fluidconduit(s) 285 disposed internal to inner electrode 205 can be used tomodulate thermionic emission from emitter material 240, as heat removalfrom inner electrode 205 modulates temperature, which, in turn, affectsthermionic emission.

Coolant can be or include a flowable liquid that exhibits phasetransition to gas at temperatures above the operating temperature ofexample reactor device 200 and phase transition to solid at temperaturesbelow the operating temperature of example reactor device 200. Forexample, where the operating temperature of a fusion plasma in chamber235 can be about 1000 K, fluid conduit(s) 285 can be configured toreceive a coolant including but not limited to molten salt, highpressure water, supercritical carbon dioxide, or other coolant systemsas described in reference to FIG. 1 .

Aperture(s) 290 can be defined at one or more points in the outerelectrode 210, such that example reactor device can be operably coupledwith an ion source, as described in more detail in reference to FIG. 3 .Aperture(s) 290 can be substantially linear and can be coupled to an ionsource via a vacuum-tight mechanical coupling, for example, with ashutter, gate valve, and/or one or more differential vacuum stagesinterposed between the ion source and chamber 235, such that ions can becontrollably injected into chamber 235 at a precise injectiontrajectory. To that end, aperture(s) 290 can define an alignmentrelative to longitudinal axis 230 that defines the injection trajectory.The injection trajectory, in turn, can correspond to a pitch angle ofentry of a stable elliptical orbit of an ion of a given mass-to-chargeratio about the inner electrode 205. In this context, the term “pitchangle of entry” describes the angle taken by a positively charged ion inthree dimensions along the alignment of aperture 290, relative tolongitudinal axis 230, where the angle corresponds to a trajectorylikely resulting in trapping the ion in an elliptical orbit about innerelectrode 205. As described previously, the injection point, kineticenergy, and pitch angle of entry can each depend on the mass-to-chargeratio of fuel ions, such that injection parameters can be preciselydetermined based on a target application using computer simulation. Inan illustrative example, ions can include protons (m/z=1), deuteriumions (m/z=2), tritium ions (m/z=3), lithium-6 ions (m/z=6), or boron-11ions (m/z=11).

Outer electrode 210 further defines port(s) 295 that extend throughouter electrode 210 and into chamber 235. Port(s) 295 can be fluidlycoupled with a vacuum system external to example reactor device 200,which can be used to create and maintain a vacuum environment betweeninner electrode 205 and outer electrode 210. A substantial vacuumcondition can be created through the one or more port(s) 295, forexample, at number densities from 1×10¹⁰ to 1×10¹⁶ atoms/cm3(corresponding to approximately 50 micro-Pa to 50 Pa). Advantageously,the vacuum thus created can improve reaction efficiency reducingcollisional losses with stray gas atoms that diffuse into chamber 235during operation.

In terms of the triple product figure of merit, higher number densitiesimplicate higher magnetic fields in chamber 235, permitting higherelectron flux to offset space charge effects, while maintainingtemperature and confinement time in ranges corresponding to a target forthe intended fusion operating regime, as described in more detail inreference to FIG. 7 . To that end, example reactor device 200 operatesat number densities from about 1×10¹¹ to about 1×10¹⁸ atoms/cm³, fromabout 1×10¹² to about 1×10¹⁸ atoms/cm³, from about 1×10¹³ to about1×10¹⁸ atoms/cm³, from about 1×10¹⁴ to about 1×10¹⁸ atoms/cm³, fromabout 1×10¹⁵ to about 1×10¹⁸ atoms/cm³, from about 1×10¹⁶ to about1×10¹⁸ atoms/cm³, from about 1×10¹⁷ to about 1×10¹⁸ atoms/cm³, includingfractions or interpolations thereof. For example, example reactor device200 can operate from about 1×10¹³ to about 1×10¹⁵ atoms/cm³ to maintainnet positive energy output from example reactor device 200. FIG. 2C is aschematic diagram illustrating example reactor device 200 incorporatinga two-part outer anode 210 in three-quarter section, in accordance withsome embodiments. The sectional view in FIG. 2C is intended toillustrate the rotational symmetry of example reactor device 200 aboutlongitudinal axis 230. As described in reference to FIG. 2A and FIG. 2B,example reactor device 200, and constituent elements such as innerelectrode 205, outer electrode 210, magnetic field generators 215, andchamber 235.

FIG. 3 is a schematic diagram illustrating an example ion injectionsystem 300, in accordance with some embodiments. Example ion injectionsystem 300 is illustrated without other components of example reactordevice 200, but it is understood that the elements described representcomponents of an example fuel ion source 110 as coupled with examplereactor device 200, configured to inject ions into chamber 235. Exampleion injection system 300 includes an ion source 305 and beam optics 310to form and inject ions 315 into chamber 235.

Ion source 305 is illustrated as a plasma-based ion source, such as aduoplasmatron, an electron cyclotron resonance device, microwave-inducedplasma device, inductively-coupled ion source or other deviceconfiguration that generates an ion-rich plasma. In some embodiments,ion source 305 includes a duoplasmatron. In the illustrative example ofa duoplasmatron, an ion beam is produced from a plasma that has beenconfined within a hollow chamber between the anode and the cathode. Theions 315 are accelerated, collimated, shaped, and/or focused using beamoptics 310 such as an Einzel lens. For example, to generate a protonbeam, a hydrogen containing source gas can be dissociated in the plasmaand the beam of hydrogen ions can be subsequently extracted by anextractor grid, shaped, collimated, and steered into aperture 290. Asimilar approach can be applied to form beams of larger ions, based onselection of the ion source gas. In some embodiments, ions 315 areinjected into chamber 235 via aperture 290, at a trajectory likelyresulting in trapping the ion 315 in an orbit 320 about inner electrode205, as described in more detail in reference to FIG. 2A and FIG. 2B.The trajectory can correspond to an angle that is tangential to asurface of the inner electrode. The tangential angle can improvetrapping efficiency and can coalesce ions 315 into orbit 320.

While the term “optics” is used, it is understood that components ofbeam optics 310 operate by application of electric fields to form ions315 into a beam and to redirect the beam of ions 315 into chamber 235via aperture 290. Similarly, while FIG. 3 illustrates only a portion ofa section through example reactor device 200 along longitudinal axis230, it is understood that in the exemplary configuration illustrated,outer electrode 210 and inner electrode 205 are rotational solids,symmetric about longitudinal axis 230.

FIG. 4 is a schematic diagram illustrating example reactor device 200and an example magnetic field generator 215 configuration, in accordancewith some embodiments. Example magnetic field generator 215configuration can be implemented in example reactor device 200, asdescribed in more detail in reference to FIG. 2A and FIG. 2B. Examplemagnetic field generator 215 configuration includes magnetic fieldgenerators 215, disposed around chamber 235 to generate a magnetic field405 substantially parallel to longitudinal axis 230 within chamber 235.

Magnetic field generators 215 can be arranged about chamber 235 suchthat within chamber 235 the polarity of magnetic field 405 is alignedwith longitudinal axis 230. In some embodiments, magnetic field 405 canbe oriented with a first polarity such that electrons emitted from innerelectrode 205 are forced to orbit in the same direction as positive ionsin accordance with the Lorentz force applied to electrons. In someembodiments, magnetic field 405 can be oriented with a second polarity,approximately opposite to the first polarity, such that electronsemitted from inner electrode 205 are forced to orbit in the opposingdirection to positive ions.

For example, at stronger magnetic field strength, in excess of the Hullcut-off condition, electrons emitted into the chamber 235 are forcedback to inner electrode 205 rapidly, avoiding a short between electrodes205 and 210 and reducing space-charge effects that in turn permitdensification of the fusion plasma. At weaker magnetic field strength,by contrast, electrons can be emitted without being deflected from outerelectrode 210 and can cause a short or an arc to form in the fusionplasma. To maintain a fusion plasma within a target range of the fusiontriple product, magnetic field 405 used to trap electrons in an orbitalpath about the inner electrode 205 within the chamber 235 can be appliedat from about 0.01 Tesla to about 10.0 Tesla, from about 0.01 Tesla toabout 9.0 Tesla, from about 0.01 Tesla to about 8.0 Tesla, from about0.01 Tesla to about 7.0 Tesla, from about 0.01 Tesla to about 6.0 Tesla,from about 0.01 Tesla to about 5.0 Tesla, from about 0.01 Tesla to about4.0 Tesla, from about 0.01 Tesla to about 3.0 Tesla, from about 0.01Tesla to about 2.0 Tesla, from about 0.01 Tesla to about 1.9 Tesla, fromabout 0.01 Tesla to about 1.8 Tesla, from about 0.01 Tesla to about 1.7Tesla, from about 0.01 Tesla to about 1.6 Tesla, from about 0.01 Teslato about 1.5 Tesla, from about 0.01 Tesla to about 1.4 Tesla, from about0.01 Tesla to about 1.3 Tesla, from about 0.01 Tesla to about 1.2 Tesla,from about 0.01 Tesla to about 1.1 Tesla, from about 0.01 Tesla to about1.0 Tesla, from about 0.01 Tesla to about 0.9 Tesla, from about 0.01Tesla to about 0.8 Tesla, from about 0.01 Tesla to about 0.7 Tesla, fromabout 0.01 Tesla to about 0.6 Tesla, from about 0.01 Tesla to about 0.5Tesla, from about 0.01 Tesla to about 0.4 Tesla, from about 0.01 Teslato about 0.3 Tesla, from about 0.01 Tesla to about 0.2 Tesla, from about0.01 Tesla to about 0.1 Tesla, or from about 0.01 Tesla to about 0.05Tesla, including fractions or interpolations thereof.

FIG. 5 is a schematic diagram illustrating an end-view representation ofthe example reactor device 200 of FIG. 2 , describing orbital paths ofemitted electrons 505 and orbiting ions 510, in accordance with someembodiments. The orbit paths illustrated are not drawn to scale, butrather are intended to illustrate concepts of the operation of examplereactor device 200. It is understood that the shape, relativedimensions, and orbiting paths indicated by arrows are illustrative andnon-limiting.

As described in more detail in reference to FIG. 2 , during operation ofexample reactor device 200, ions 510 are injected tangentially betweeninner electrode 205 and outer electrode 210 and into an electrostaticfield with sufficient energy to assume stable elliptical orbits aroundinner electrode 205. During an elliptical orbit 520, ions 510 acceleratetowards the negatively biased inner electrode 205, converting potentialenergy into kinetic energy, until reaching the perigee point of theelliptical orbit 520. After reaching perigee, ions 510 decelerate whilemoving away from the negative cathode potential and storing potentialenergy until reaching the apogee point of the elliptical orbit 520. Ions510 can complete millions of elliptical orbits 520 in the reactor over aperiod of time on the order of one second. Additionally, the ellipticalion orbit 520 can exhibit apsidal precession around the central cathode205 such that elliptical orbits 520 of ions 510 can cross ellipticalorbits of other ions 510 up to and exceeding millions of times,increasing the probability of a relatively unlikely fusion event 525 tooccur. Eventually, collisions between ions 510 in overlapping orbitaltrajectories result in fusion events 525, releasing fusion reactionproducts, including but not limited to charged particles (alphas,helium-3, protons, tritium, etc.), radiation, and thermal energy.

Inner electrode 205, including emitter material 240, injects electrons505 into chamber 235. Through interaction with magnetic field 405,electrons 505 are bent into partial orbits around inner electrode 205,eventually returning to inner electrode 205. In some embodiments,emitter material 240 is an isotropic emitter, such that electrons areemitted in all radial directions substantially equally, which isdemonstrated by multiple electron orbital paths 515. As a result, theinfluence of electrons 505 on ion 510 density in chamber 235 can besubstantially uniform about inner electrode 205. Advantageously,maintaining a substantially symmetrical electron 505 distribution aboutinner electrode 205 can reduce self-structuring in plasmas that mayinhibit nuclear fusion, induce arc runaway, or introduce otheroperational issues.

FIG. 6 is a graph 600 illustrating reaction rate (ordinate) and iondensity (abscissa) for an example orbital confinement reactor device 105in accordance with some embodiments. Graph 600 illustrates differentoperating regimes 605 characterized by different ion density, measuredin atoms/cm³, and reaction rate, measured in fusion events per second,plotted along an operating curve 610 describing an illustrativeoperational window of example device 105. It is understood that thedetails described in reference to example reactor device 200, such asoperating parameters, internal structures, and material configurationscan be configured such that example system 100 operates in one or moreof the operating regimes 605. The operating regimes 605 correspond todifferent applications as described in more detail in reference to FIG.1 . For example, graph 600 includes a first regime 605-1, where exampledevice 105 operates as a neutron generator applied, for example, toneutron-based imaging. A second regime 605-2 describes operation as ahigh-flux neutron generator, for example, in isotope production formedical use. A third regime 605-3 describes operation as a compact powersource, whereby the reaction rate and ion density are high enough togenerate net-positive energy out of the example device 105.

As described in more detail in reference to the FIGS. 1-5 , operatingregimes 605 are not discrete, but rather are included as examples withinthe range of operating curve 610 to illustrate the dependency ofreaction rate on ion density, for a given set of conditions. Forexample, operating curve 610 can describe the relationship between iondensity and reaction rate for a given electron temperature, operatingpressure, magnetic field strength, etc. For graph 600, operating curve610 describes values of reaction rate and ion density for an exampledevice 105 operating at 125 keV average electron temperature.

Graph 600 illustrates that example device 105 can operate as a neutronsource and/or as a power source, but that different operating regimes605 can implicate different operating parameters and configurations.Structurally, a specialized neutron generator device can exclude one ormore components used to extract power from the fusion plasma, includingbut not limited to image current circuit 250, dielectric insulator 255,or compound outer electrode shells 210-1 and 210-2. Graph 600 alsoillustrates the influence of ion density on ion temperature, and how iondensity and ion temperature are correlated with recirculation frequencyand fusion cross section (a), as described in more detail in referenceto the theoretical introduction above.

Advantageously, net fusion power exceeding 1 kW, corresponding to thirdoperating regime 605-3, can be generated by example device 105 having achamber size on the order of 10 cm. Chamber size can be described by arange within which example device 105 operates as described in referenceto FIG. 6 . For example, the inner radius, corresponding to the radiusof inner electrode, can be from about 0.1 cm to about 40.0 cm. As theinner radius decreases, however, the electron flux and/or number ofelectrons injected from emitter material 240 into chamber 235 may alsodecrease such that the design approaches that of the Kingdon trap, whichbecomes limited in its electron emission due to reduced surface area,and thus the number of fusion events that can take place per givenperiod of time does not generate net positive energy output. Incontrast, where the distance between inner electrode 205 and outerelectrode 210 is relatively small, loss mechanisms such as ion collisionwith inner electrode 205, Bremsstrahlung losses, and electron arcing orshorting with outer electrode 210 become significant, thereby reducingfusion reaction rate. In this way, inner electrode can have a radiusranging from about 0.1 cm to about 40.0 cm, from about 0.1 cm to about30.0 cm, from about 0.1 cm to about 20.0 cm, from about 0.1 cm to about15.0 cm, from about 0.1 cm to about 10.0 cm, from about 0.1 cm to about9.5 cm, from about 0.1 cm to about 9.0 cm, from about 0.1 cm to about8.5 cm, from about 0.1 cm to about 8.0 cm, from about 0.1 cm to about7.5 cm, from about 0.1 cm to about 7.0 cm, from about 0.1 cm to about6.5 cm, from about 0.1 cm to about 6.0 cm, from about 0.1 cm to about5.5 cm, from about 0.1 cm to about 5.0 cm, from about 0.1 cm to about4.5 cm, from about 0.1 cm to about 4.0 cm, from about 0.1 cm to about3.5 cm, from about 0.1 cm to about 3.0 cm, from about 0.1 cm to about2.5 cm, from about 0.1 cm to about 2.0 cm, from about 0.1 cm to about1.5 cm, from about 0.1 cm to about 1.0 cm, or from about 0.1 cm to about0.5 cm, including fractions and interpolations thereof.

Analogously, the dimensions of outer electrode 210 are similarlycharacterized by a range within which example device 105 operates asdescribed in reference FIG. 6 . For example, the outer radius,corresponding to the radius of outer electrode 210 facing chamber 235,can be from about 1 cm to about 20 cm. As the outer radius decreases,the electron flux into outer electrode 205 may increase, such that theeffect of electron injection on space charge is mitigated, reducing theion density and shifting the device to the left on operating curve 610.Similarly, when outer radius increases, the energy needed to maintaincompact orbits for ions and electrons increases, as the distance betweenchamber 235 and magnetic field generators 215 increases. In this way,outer electrode can have a radius ranging from about 1 cm to about 100cm, from about 1 cm to about 90 cm, from about 1 cm to about 80 cm, fromabout 1 cm to about 70 cm, from about 1 cm to about 60 cm, from about 1cm to about 50 cm, from about 1 cm to about 40 cm, from about 1 cm toabout 30 cm, from about 1 cm to about 20 cm, from about 1 cm to about 19cm, from about 1 cm to about 18 cm, from about 1 cm to about 17 cm, fromabout 1 cm to about 16 cm, from about 1 cm to about 15 cm, from about 1cm to about 14 cm, from about 1 cm to about 13 cm, from about 1 cm toabout 12 cm, from about 1 cm to about 11 cm, from about 1 cm to about 10cm, from about 1 cm to about 9 cm, from about 1 cm to about 8 cm, fromabout 1 cm to about 7 cm, from about 1 cm to about 6 cm, from about 1 cmto about 5 cm, from about 1 cm to about 4 cm, from about 1 cm to about 3cm, or from about 1 cm to about 2 cm, including fractions andinterpolations thereof

FIG. 7 is a block diagram illustrating an example process 700 forgenerating energy or neutrons using an orbital confinement reactordevice, in accordance with some embodiments. The blocks of exampleprocess 700 represent operations that can be implemented autonomously(e.g., without human intervention) by a computing device. The computingdevice can be or include control circuitry operably coupled with thecomponents of the orbital confinement reactor device, such as examplereactor device 200 of FIG. 2A, FIG. 2B, and FIG. 2C, such that theoperations of example process 700 can be dynamically controlled in termsof timing, frequency, and/or magnitude, as part of a control scheme tomaintain criticality (e.g., k≈1) of nuclear fusion in chamber 235. Assuch, it is understood that some of the operations illustrated in FIG. 7can be omitted, reordered, and/or repeated, depending, for example, onthe target application of example reactor device 200.

At block 705, example process 700 includes energizing inner electrode205. The voltage applied to inner electrode 205, for example, by highvoltage power source 220, can be from 50 kV DC to about 4.0 MV DC,including fractions thereof, as described in more detail in reference toFIG. 2A. Energizing inner electrode 205 serves to trap ions intoelliptical orbits about longitudinal axis 230, as described in moredetail in reference to FIG. 5 , and also serves to increase emission ofelectrons from emitter material 240 by field emission. Heating of innerelectrode 205 can increase electron emission from the emitter material240 through thermionic emission. Heating can be active, throughresistive heating elements or by resistive heating of emitter material240, or can be passive through electron and ion collisions with innerelectrode 205.

At block 710, example process 700 includes injecting ions into chamber235. As described in more detail in reference to FIG. 3 , ions 315 canbe injected into chamber 235 at an angle tangential to a surface of theinner electrode. Injection at the tangential angle can cause the ions tointeract with the electrostatic field and enter orbit 320 about theinner electrode 205. Injecting ions can be an intermittent or acontinuous process, as part of maintaining criticality by managing ionenergy and population parameters during operation of example reactordevice 200. In some embodiments, ion injection can be manipulated as acontrol variable as part of a closed loop control system.

At block 715, example process 700 includes generating magnetic field 405in chamber 235. Magnetic field 405 can be generated by magnetic fieldgenerators 215, aligned with longitudinal axis 230, using an arrangementof magnetic field generators 215 that creates a magnetron in chamber235. As part of trapping electrons in chamber 235, magnetic field 405can be characterized by an intensity corresponding to a Hull cut-offcondition that redirects the electrons back toward inner electrode 205.As described in more detail in reference to FIG. 5 , electron orbits 515can be partial, such that electrons may form a substantially circularorbit that does not complete a circuit about inner electrode 205,although complete orbits of electrons may occur.

In some embodiments, example process 700 can optionally include flowingcoolant through conduits 285. Where power dissipation in example reactordevice 200 generates heat, flowing coolant through conduits 285 canextract thermal energy from fusion reactions and can serve as a controlparameter to maintain stable reactor operation. As described in moredetail in reference to FIG. 1 , heat removed from example reactor device200 can be converted to electricity using thermoelectric generators,turbines, or the like, or can be used for heat through coupling withheat exchangers. In some embodiments, the coolant can be or includematerials that are liquid at elevated temperature and/or pressure, suchas up to and including 1000 K.

As part of power generation in the context of example system 100 of FIG.1 , example process 700 can optionally include applying an RF voltagesignal to outer electrode 210 at block 725. Axial harmonic motion oforbiting ions can be damped by application of RF voltage to imagecurrent circuit 250. In this way, electricity can be directly extractedfrom fusion plasmas and can be transformed into usable electricity bypower electronics, including but not limited to inverters or rectifiers.

As such, using heat and electrical energy extracted from example device,example process 700 can optionally include converting energy toelectricity at block 730. For example, where example reactor device 200is operating as a power source (e.g., third operating regime 605-3 ofFIG. 6 ), net fusion power out of the example device 200 can beconverted to electricity for distribution to the grid and/or for storagein capacitors, batteries, pumped storage, or the like. In contrast,where example reactor device 200 is operating as a neutron source,direct electrical generation of block 725 can be omitted and examplereactor device 200 can operate without connection to thermal generators120.

The processes explained above are described in terms of computersoftware and hardware. The techniques described may constitutemachine-executable instructions embodied within a tangible ornon-transitory machine (e.g., computer) readable storage medium, thatwhen executed by a machine will cause the machine to perform theoperations described. Additionally, the processes may be embodied withinhardware, such as an application specific integrated circuit (“ASIC”) orotherwise.

A tangible machine-readable storage medium includes any mechanism thatprovides (i.e., stores) information in a non-transitory form accessibleby a machine (e.g., a computer, network device, personal digitalassistant, manufacturing tool, any device with a set of one or moreprocessors, etc.). For example, a machine-readable storage mediumincludes recordable/non-recordable media (e.g., read only memory (ROM),random access memory (RAM), magnetic disk storage media, optical storagemedia, flash memory devices, etc.).

The above description of illustrated embodiments of the invention,including what is described in the Abstract, is not intended to beexhaustive or to limit the invention to the precise forms disclosed.While specific embodiments of, and examples for, the invention aredescribed herein for illustrative purposes, various modifications arepossible within the scope of the invention, as those skilled in therelevant art will recognize.

These modifications can be made to the invention in light of the abovedetailed description. The terms used in the following claims should notbe construed to limit the invention to the specific embodimentsdisclosed in the specification. Rather, the scope of the invention is tobe determined entirely by the following claims, which are to beconstrued in accordance with established doctrines of claiminterpretation.

The invention claimed is:
 1. A method of generating orbital confinementfusion energy in a fusion device, wherein the fusion device comprises: acathodic inner electrode defining a longitudinal axis of the device, theinner electrode comprising an emitter material; an anodic outerelectrode, concentric with the longitudinal axis and defining a chamberbetween the inner electrode and the outer electrode; and a plurality ofmagnetic field generators disposed in a coaxial arrangement relative tothe longitudinal axis of the device, the plurality of magnetic fieldgenerators configured to form a magnetron; and wherein the methodcomprises: energizing the inner electrode to a voltage from about 50 kVDC to about 4.0 MV DC, thereby forming a logarithmic electrostatic fieldbetween the inner electrode and the outer electrode and injecting aplurality of electrons into the chamber; injecting a beam of fuel ionsinto the chamber and at an angle tangential to a surface of the innerelectrode, causing the fuel ions to interact with the electrostaticfield and to enter an elliptical orbit about the inner electrode; andgenerating a magnetic field aligned with the longitudinal axis using theplurality of magnetic field generators, the magnetic field characterizedby an intensity corresponding to a Hull cut-off condition andredirecting the electrons back toward the inner electrode.
 2. The methodof claim 1, wherein the fusion device further comprises a fluid conduitformed in the inner electrode or the outer electrode, the method furthercomprising: flowing a coolant through the fluid conduit; heating thecoolant through contact with the outer electrode; and generatingelectricity using the heated coolant.
 3. The method of claim 1, furthercomprising: applying a radio-frequency (RF) voltage signal to the outerelectrode using a charge image circuit, wherein a frequency of the RFvoltage signal corresponds to an oscillation of charged particles in thechamber along a direction aligned with the longitudinal axis; generatingan RF current using the charge image circuit; and generating a directcurrent from the RF current using an RF-to-DC rectifier circuit.
 4. Themethod of claim 1, wherein the inner and outer electrodes are solids ofrevolution, symmetric about the longitudinal axis, and are shaped toform a substantially logarithmic electrostatic field in the chamber whenenergized.
 5. The method of claim 1, wherein the inner electrode ischaracterized by an aspect ratio greater than one along the longitudinalaxis, and wherein the outer electrode has a length along thelongitudinal axis greater than a largest diameter of the innerelectrode.
 6. The method of claim 1, wherein the outer electrodecomprises: a first anode shell and a second anode shell, disposedlaterally relative to the longitudinal axis; and a dielectric insulatordisposed between and electrically isolating the first anode shell andthe second anode shell.
 7. The method of claim 1, wherein the magneticfield is characterized by a magnetic field strength exceeding a Hullcut-off condition to trap electrons in an orbital path about the innerelectrode within the chamber.
 8. The method of claim 1, wherein theplurality of magnetic field generators comprises permanent magnets. 9.The method of claim 1, wherein the plurality of magnetic fieldgenerators comprises electromagnets.
 10. The method of claim 1, whereinthe inner electrode defines a first end and a second end, the devicefurther comprising: a first dielectric insulator mechanically coupledwith the first end and isolating the first end from the outer electrode;and a second dielectric insulator disposed in the chamber between thesecond end and the outer electrode and isolating the second end from theouter electrode.
 11. The method of claim 10, wherein the firstdielectric insulator defines an insulating cavity and electricallyisolates the high voltage power source from the outer electrode.
 12. Themethod of claim 1, wherein the outer electrode defines an aperture, analignment of the aperture defining an injection trajectory, theinjection trajectory corresponding to a pitch angle of entry of a stableelliptical orbit of an ion of a given mass-to-charge ratio about theinner electrode.
 13. The method of claim 12, wherein the ion is a proton(m/z=1), a deuterium ion (m/z=2), a tritium ion (m/z=3), lithium-6 ion(m/z=6), or a boron-11 ion (m/z=11).
 14. The method of claim 1, whereinthe outer electrode further defines a port fluidly coupled with thechamber and an external environment, the port being configured tofluidly couple with a vacuum system.
 15. The method of claim 1, whereinthe emitter material is disposed on the inner electrode or integrated inthe inner electrode, and wherein the emitter material is configured toinject electrons into the chamber when the inner electrode is energized.16. The method of claim 1, wherein the emitter material is a thermionicemitter material.
 17. The method of claim 1, wherein the device ischaracterized by physical dimensions on the order of tens ofcentimeters.
 18. The method of claim 1, wherein the device iselectrically coupled with an electrical power system configured toreceive electrical power or heated coolant from the device.